Two car bombs targeting Christians killed at least 38 people in southern Baghdad on Christmas .

In Afghanistan , two rounds of `` indirect fire '' hit the U.S. Embassy compound in Kabul , but no one was hurt .

The incidents highlight the security challenges with which both Iraq and Afghanistan are grappling .

Both countries have had a heavy U.S. military presence until recently .

The departure of U.S. forces from Iraq has done little to curb the near-daily cycle of violence . In Afghanistan , U.S. and Afghan officials are working on an important security pact to outline the future of American troops in Afghanistan .

18 dead in Christmas Day attacks near Iraq churches

Iraq attacks

In Iraq , a car bomb exploded outside a church in southern Baghdad just as worshipers were leaving a Christmas Day service , killing many . In another attack Wednesday , a car bomb went off at an outdoor market where many Christians shop , police said .

Altogether , at least 38 people were killed and some 70 others were wounded , the Interior Ministry said . The bomb outside the church killed 27 and wounded 56 . The market attack left 11 dead and 14 wounded .

The U.S. Embassy in Baghdad condemned the attacks -- in the Dora area of Baghdad -- targeting `` Christians celebrating Christmas . ''

`` The Christian community in Iraq has suffered deliberate and senseless targeting by terrorists for many years , as have many other innocent Iraqis . The United States abhors all such attacks and is committed to its partnership with the Government of Iraq to combat the scourge of terrorism , '' according to a statement released by the embassy .

Iraq has experienced an uptick in sectarian violence this year as tensions simmer between the disaffected minority Sunni community and the Shiites , who dominate the government .

The U.S. Commission on International Religious Freedom notes that many people in small religious minority communities in Iraq , including Christians , have fled the country over the last decade and those that remain are `` particularly vulnerable , '' facing `` discrimination , marginalization , and neglect . ''

Sectarian warfare , especially between Sunnis and Shiites , raged during the Iraq War . Half or more of the pre-2003 Iraqi Christian community is thought to have left Iraq , the commission said in its 2013 annual report .

In 2003 , there were thought to be 800,000 to 1.4 million Chaldean Catholics , Assyrian Orthodox , Assyrian Church of the East members , Syriac Catholics and Orthodox , Armenian Catholics and Orthodox , Protestants and evangelicals in the country , the group said .

Now , according to community leaders , the estimated number of Christians stands at around 500,000 , the report said .

Afghanistan attack

Two rounds of `` indirect fire '' hit the U.S. Embassy compound in Kabul , the embassy said . No one was injured .

`` At approximately 6:40 local time in Kabul , approximately two rounds of indirect fire impacted the U.S. Embassy compound . All Americans are accounted for and no injuries were sustained , '' the embassy said in a statement Wednesday . `` The Embassy continues to investigate the attack . ''

The embassy did not elaborate on what kind of rounds were fired , or where in the compound they landed .

A claim of responsibility was posted on the Taliban 's official website . The group said it fired missiles at the U.S. Embassy and the main base of NATO , which leads the military coalition known as the International Security Assistance Force .

The incident comes at a pivotal time in U.S.-Afghan relations . The two countries are working on an important security pact . The deal will lay out the U.S. military presence in Afghanistan after 2014 when the NATO-led force of some 80,000 troops is scheduled to leave .

This month , U.S. Defense Secretary Chuck Hagel was in Afghanistan and said the security pact will be agreed upon despite a failure so far to forge a deal .

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U.S. Embassy condemns `` senseless targeting '' of Christians and other Iraqis

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In Iraq , a car bomb explodes outside a church after Christmas services ; another targets market

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Taliban claim responsibility for the embassy attack in Kabul , Afghanistan

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Many Christians have fled Iraq over the past decade , report says